Many computer-based engineering models use finite element discretization based models to model and simulate the behavior of three-dimensional objects. A popular choice for many such engineering models involves the use of hexahedral meshes (hex-meshes) as the finite element discretization of choice. Typical, but non-limiting examples of input objects which may be modelled using hex-meshes include: parts of mechanical systems; fluid conduits for fluid simulation; biological elements, such as human bones and/or organs. There is a general desire to provide high quality hex-meshes, since the quality of such hex-meshes can influence the accuracy and/or reliability of the corresponding engineering models. The generation of hex-meshes is typically a two-step process which involves: (i) generating an initial hex-mesh whose connectivity is designed to fit the input object; and (ii) modifying the positions of vertices to optimize the shapes of the mesh elements while keeping the connectivity fixed.
A challenge that is faced by automated (computer-based) hex-mesh generation techniques is that the generated hex-meshes typically contain poorly shaped hexahedrons. For example, poorly shaped hexahedrons may comprise hexahedrons that are relatively far from cuboid in shape and/or hexahedrons that are inverted or concave in shape. Even a single inverted (concave) hexahedral element can render an entire hex-mesh representation unusable for simulation. Hex-meshes comprising such poorly shaped hexahedrons may be referred to as low quality hex-meshes and individual poorly shaped hexahedrons within such hex-meshes may be referred to as low quality hexahedrons or low quality elements. There is a general desire for automated computer-based techniques for improving the quality of hex-meshes (e.g. hex-mesh representations of input objects). Such hex-mesh improvement techniques may improve the average quality of the hex-mesh elements and/or the minimum quality of the hex-mesh elements and may be referred to as hex-mesh optimization techniques.
The foregoing examples of the related art and limitations related thereto are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the description and a study of the drawings.